Osterwalder-Schrader axioms for unitary full vertex operator algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914903345856512 |
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| author | Adamo, Maria Stella Moriwaki, Yuto Tanimoto, Yoh |
| author_facet | Adamo, Maria Stella Moriwaki, Yuto Tanimoto, Yoh |
| contents | Full Vertex Operator Algebras (full VOA) are extensions of two commuting Vertex Operator Algebras, introduced to formulate compact two-dimensional conformal field theory. We define unitarity, polynomial energy bounds and polynomial spectral density for full VOA. Under these conditions and local $C_1$-cofiniteness of the simple full VOA, we show that the correlation functions of quasi-primary fields define tempered distributions and satisfy a conformal version of the Osterwalder-Schrader axioms, including the linear growth condition.
As an example, we show that a family of full extensions of the Heisenberg VOA satisfies all these assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Osterwalder-Schrader axioms for unitary full vertex operator algebras Adamo, Maria Stella Moriwaki, Yuto Tanimoto, Yoh Mathematical Physics Quantum Algebra Representation Theory 81T05, 81T40, 17B69 Full Vertex Operator Algebras (full VOA) are extensions of two commuting Vertex Operator Algebras, introduced to formulate compact two-dimensional conformal field theory. We define unitarity, polynomial energy bounds and polynomial spectral density for full VOA. Under these conditions and local $C_1$-cofiniteness of the simple full VOA, we show that the correlation functions of quasi-primary fields define tempered distributions and satisfy a conformal version of the Osterwalder-Schrader axioms, including the linear growth condition. As an example, we show that a family of full extensions of the Heisenberg VOA satisfies all these assumptions. |
| title | Osterwalder-Schrader axioms for unitary full vertex operator algebras |
| topic | Mathematical Physics Quantum Algebra Representation Theory 81T05, 81T40, 17B69 |
| url | https://arxiv.org/abs/2407.18222 |